If `u=a-b` and `v=a+b` and `|a|=|b|=2`, then `|uxx v|` is equal to

Options

A. `2sqrt(16-(a.b)^(2))`
B. `sqrt(16-(a.b)^(2))`
C. `2sqrt(4-(a.b)^(2))`
D. `2sqrt(4+(a.b)^(2))`

Answer

A

Explanation

Now, `|uxxv|=(a-b)xx(a+b)=2|=2||axxb|`
`[because axxa =bxxb=0]`
and `|axxb|^(2)+(a*b)^(2)=(ab sin theta)^(2)+(ab cos theta)^(2)=a^(2)b^(2)`
`|axxb|=sqrt(a^(2)b^(2)-(a*b)^(2))`
So`|uxxv|=2|axxb|=2sqrt(a^(2)b^(2)-(a*b)^(2))`
`=2sqrt(2^(2)2^(2)-(a*b)^(2))`
`=2sqrt(16-(a*b)^(2))[because |a|=|b|=2]`